Symmetric Level Index Arithmetic in Simulation and Modeling

This paper begins with a general introduction to the symmetric level-index, SLI, system of number representation and arithmetic. This system provides a robust framework in which experimental computation can be performed without the risk of failure due to overflow/underflow or to poor scaling of the original problem. There follows a brief summary of some existing computational experience with this system to illustrate its strengths in numerical, graphical and parallel computational settings. An example of the use of SLI arithmetic to overcome graphics failure in the modeling of a turbulent combustion problem is presented. The main thrust of this paper is to introduce the idea of SLI-linear least squares data fitting. The use of generalized logarithm and exponential functions is seen to offer significant improvement over the more conventional linear regression tools for fitting data from a compound exponential decay such as the decay of radioactive materials.